Updated with data available as of April 25, 2020

Summary

Aims

The USC Predict COVID project is using an epidemic model to estimate the impact of COVID-19 in Los Angeles County

We are addressing the key questions of:

  • When will the peak of the epidemic occur and how will it impact health care capacity?
  • What happens to the dynamics of the epidemic when social distancing ends?
  • How will the epidemic affect different at-risk groups?

Why our model is unique

  • Our epidemic compartmental model uses stochastic differential equations and approximate Bayes calculation techniques for parameter estimation.
  • Importantly, the model presents the uncertainty in all estimations and predictions.
  • We incorporate prior information for parameter specification.
  • We incorporate risk factors (e.g. advanced age, existing health conditions) into the analysis.
  • We can modify parameters at different time points, enabling the specification of interventions, e.g. social distancing scenarios

Predictions and Estimation

(1) Critical healthcare variables predicted by the model are the counts of the numbers of individuals over time, including the peak occurrence, for the following:

  • The total number of infected cases including both the number detected and observed with testing and the undetected/untested cases
  • The total number of individuals hospitalized (including those in the ICU)
  • The number of patients in the ICU
  • The number of patients on ventilators
  • The number of deaths

(2) We estimate a number of key epidemic parameters, including:

  • \(R0\), the reproductive number or average number of new infections generated by an infected person in a completely susceptible population
  • \(r\), the proportion of illnesses that are detected and reported out of all illnesses
  • \(Frac_{R0}\), the reduction in the initial R0 due to social distancing
  • \(\alpha\), the probability of hospitalization given illness, i.e. \(Pr(Hospital | Illness)\)
  • \(\kappa\), the probability of ICU care necessary given hospitalization, i.e. \(Pr(ICU | Hospital)\)
  • \(p_v\), the probability of ventilation given ICU care, i.e. \(Pr(Ventilation | ICU)\)
  • \(\delta\), the probability of death given ICU care, i.e. \(Pr(Death | ICU)\)

(3) We also provide predictions for the impact on counts and corresponding time periods under various social distancing scenarios in which restrictions are eased.

Projections

Current Projections: Summary of Key Model Estimated Variables

Median Upper 50 CI Lower 50 CI
Peak Hospitalizations 6,086.00 9,727.00 2,558.00
Deaths by August 1, 2020 21,562.50 31,506.25 12,798.75
Detected Illnesses by August 1,2020 622,988.00 900,654.75 362,311.00
Total Illnesses by August 1, 2020 5,428,588.50 6,715,058.50 3,217,905.50
Proportion of Cases Detected (%) 13.22 16.04 10.45
CFR Based on Observed Illnesses (%) 3.87 4.74 2.78
CFR Based on Total Illnesses (%) 0.48 0.62 0.35
R0 - before social distancing 3.38 3.79 2.96
% Reduction in Social Contacts (March 15 - ) 59.82 54.26 63.59

Current Projections: Illnesses, Hospitalizations, ICU Admittances, Ventilation Requirements, Deaths

Dashed line = Maximum possible capacity (i.e., total licensed hospital beds, ICU beds, ventilators) in L.A. County

Model Fits Against Data

Demonstrating model fit against COVID-19 data for Los Angeles, for the following variables:

COVID-19 data is shown as black dots in the figures below.

Comparing Social Distancing Mitigation Strategies

Scenario Comparison

Comparison between current level of social distancing of ~50% beginning March 15, 2020 and counterfactual: if social distancing had never been implemented

Comparison between current level of social distancing of ~50% beginning March 15, 2020 and easing of social distancing from 50% to 25% on May 1, 2020

Comparison between current level of social distancing of ~50% beginning March 15, 2020 and easing of social distancing from 50% to 25% on June 1, 2020

Comparison between current level of social distancing of ~50% beginning March 15, 2020 and easing of social distancing from 50% to 25% on July 1, 2020

Comparison between current level of social distancing of ~50% beginning March 15, 2020 and removal of social distancing on June 1, 2020

Comparison between policy of easing of social distancing from 50% to 25% on June 1, 2020 and gradual easing beginning June 1, 2020 of social distancing from 50% to no social distancing

Projections by Key Risk Groups and Risk Factors

Risk Profiles, Risk Factors, and Risk Groups

  • The following table presents the model-estimated probabilities \(Pr(Hospital | Illness,Profile_i)\), \(Pr(ICU | Hospital,Profile_i)\), and \(Pr(Death | ICU,Profile_i)\) for each risk group (or combination of risk factors), as well as the prevalence of these risk groups/factors in the general L.A. County Population \(Pr(Profile_i)\).

5 Risk Groups by Stage of Disease and SPA

  • These figures show the estimated proportion of each risk group that will make up the resulting cohorts of COVID patients admitted to hospital, admitted to ICU, or that die within the L.A. County/SPA population, based on the population prevalence of the risk group in L.A. County/SPAs.
  • The analyses are presented for each risk group, as well as stratified to the individual risk factors (age, comorbidities, obesity status, smoking status).

Trajectories: Hospitalizations, ICU, Deaths by Key Risk Factors LA County

Parameter estimates

Model estimated parameters and prior information

Here we summarize our estimated parameter values for key epidemic and model quantities:

  • \(R0\), the reproductive number or average number of new infections generated by an infected person in a completely susceptible population
  • \(r\), the proportion of illnesses that are observed
  • \(Frac_{R0}\), the reduction in the initial R0 due to social distancing
  • \(\alpha\), the probability of hospitalization given illness, i.e. \(Pr(Hospital | Illness)\)
  • \(\kappa\), the probability of ICU care necessary given hospitalization, i.e. \(Pr(ICU | Hospital)\)
  • \(p_v\), the probability of ventilation given ICU care, i.e. \(Pr(Ventilation | ICU)\)
  • \(\delta\), the probability of death given ICU care, i.e. \(Pr(Death | ICU)\)

Because our model is stochastic and we are using Bayesian techniques for parameter estimation, each posterior parameter estimate is represented by a distribution of likely values.

This table summarizes key statistics of each estimated parameter: the mean and the standard deviation (sd).

R0 Prop. cases detected (r) Frac R0 Mar11 Pr(Death|ICU) Pr(Hospital|Illness) Pr(ICU|Hospital) Pr(Ventilation|ICU) Frac R0 Apr23
mean 3.36 0.14 0.42 0.54 0.21 0.36 0.74 0.40
sd 0.61 0.05 0.06 0.16 0.03 0.04 0.08 0.06
  • Mean = 3.36
  • Standard deviation = 0.61

Information informing prior distribution - \(R0\) prior estimate is based on values for \(R0\) estimated from other published studies on COVID-19.

  • Mean = 0.14
  • Standard deviation = 0.05

  • Mean = 0.42
  • Standard deviation = 0.06

Information informing this parameter’s prior distribution:

We use previous studies to narrow the specification of the probability of hospitalization given illness, admittance to the intensive care unit (ICU) given being in hospital, ventilation given being in ICU, and death given being in ICU by incorporating risk factors, including age, sex, smoking and other comorbidities. The prevalence of these risk factors in Los Angeles County is also included.

Studies on COVID-19 clinical presentation and trajectories to inform the probability of hospitalization, ICU, and ventilation based on single risk factors: - Guan, Wei-jie, et al. “Clinical characteristics of coronavirus disease 2019 in China.” New England Journal of Medicine (2020). - Petrilli, Christopher M., et al. “Factors associated with hospitalization and critical illness among 4,103 patients with COVID-19 disease in New York City.” medRxiv (2020).

Prevalence data sources: - Los Angeles County Health Survey - UCLA California Health Information Survey

  • Mean = 0.21
  • Standard deviation = 0.03

  • Mean = 0.36
  • Standard deviation = 0.04

  • Mean = 0.54
  • Standard deviation = 0.16

  • Mean = 0.74
  • Standard deviation = 0.08